Electron cooling in a magnetically expanding plasma, which is a fundamental process for plasma flow and detachment in magnetic nozzles, is experimentally investigated using a radio frequency plasma source and magnetic nozzle (MN). Probe measurements of the plasma density, potential, and electron temperature along the center line of the MN indicate that the expansion follows a polytropic law with exponent γ_{e}=1.15±0.03. This value contradicts isothermal electron expansion, γ_{e}=1, which is commonly assumed in MN models. The axial variation of the measured quantities can be described by a simple quasi-1D fluid model with classical electron thermal conduction, for which it has been previously shown that a value of γ_{e}≈1.19 is expected in the weakly collisional limit. A new criterion, derived from the model, ensures efficient ion acceleration when a critical value for the ratio of convected to conducted power is exceeded.